Physics Help Needed!

Question

1. ) A 100 gram marble strikes squarely against a 30.0 gram marble which is lying at rest on a flat, smooth surface. During the impact, the speed of the large marble is reduced from 90.0 cm/sec to 50 cm/sec. What is the speed of the small marble immediately following the impact?

2.) A 5.5 kilogram double barreled shotgun simultaneously fires 25 grams of shot from each barrel with a muzzle velocity of 200 m/sec. Find the shotgun's recoil velocity

Answer 1

Conservation of Momentum:

Initial Momentum = Final Momentum

m1v1 initial + m2v2 initial = m1v1 final + m2v2 final

m1 = 100 grams

m2 = 30 grams

v1 initial = 90 cm/sec

v1 final = 50 cm/sec

v2 initial = at rest = 0 cm/sec

v2 final = ?

We are plugging in our knowns into the equation to find the missing v2 final

*These numbers are not in the correct units but as long as they are all in the same units then your answer will come out with the same units —> all our masses are in grams and all our velocities are in cm/sec so our answer v2 final will come out in cm/sec

(100)(90) + (30)(0) = (100)(50) + (30)v2final

9000 + 0 = 5000 + 30v2final

subtract 5000 from both sides

4000 = 30v2final divide by 30

v2f = 133.33 cm/sec

#2

mass of gun = 5.5 kg

mass of each bullet = 25 g

velocity of each bullet = 200 m/sec

the masses are in different units so I am going to convert grams to kilograms by dividing by 1000

mass each bullet = 0.025 kg

we have 3 objects in this system, one gun and 2 bullets, and all of them are initially not moving

m1 = 5.5 kg

m2 = 0.025 kg

m3 = 0.025 kg

v1 initial = v2 initial = v3 initial = 0 m/sec

v1 final = ?

v2 final = v3 final = 200 m/sec

Plug into the conservation of momentum equation and solve for v1 final

(5.5)(0) + (0.025)(0) + (0.025)(0) = (5.5)v1 final + (0.025)(200) + (0.025)(200)

0 + 0 + 0 = 5.5v1final + 5 + 5

0 = 5.5v1 final + 10 subtract 10 from both sides

-10 = 5.5v1final divide by 5.5

v1 final = - 1.82 m/sec

It makes sense that it’s negative because the gun would go backward to recoil if the bullets are going forward.